A salesman sells an article at 8% loss. Had he bought the article at 12% less and and sold it at 26 more, he would have made a profit of $11\dfrac{1}{9}$% Find the new selling price of the article.

Solution: Let the cost price of the article be 100c

Selling price of the article = 92 c

New cost price = 88c

New selling price = 92c + 26

Given

$92c + 23 = \dfrac{10}{9}\times88c \rightarrow c = 4.5$

$\therefore$ Required new selling price
= 92 x 4.5 + 26 = 440

I have two questions:

How new selling price is 92c + 26 rather than 88c + 26?

"sold it at 26 more", in English, means sold it for 26 more than he had sold it for in the first scenario. So this is 26 more than the 92c he had sold it for in the first place, not 26 more than the cost.

Quote:

How $\dfrac{10}{9}$ is obtained?

$1+ 11\frac{1}{9}%= (100+ \frac{100}{9})%= \frac{1000}{9}%$ which, dividing by 100 (since it is a "percent") is $\frac{10}{9}$.